https://github.com/cheind/monte-carlo-integration

Theory and implementation of Monte Carlo integration techniques
https://github.com/cheind/monte-carlo-integration

monte-carlo-integration python theory

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Theory and implementation of Monte Carlo integration techniques

• Host: GitHub
• URL: https://github.com/cheind/monte-carlo-integration
• Owner: cheind
• License: mit
• Created: 2022-06-24T03:41:42.000Z (about 4 years ago)
• Default Branch: main
• Last Pushed: 2022-08-21T09:25:06.000Z (almost 4 years ago)
• Last Synced: 2024-10-16T04:06:42.343Z (over 1 year ago)
• Topics: monte-carlo-integration, python, theory
• Language: Python
• Homepage:
• Size: 873 KB
• Stars: 4
• Watchers: 1
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.7013396.svg)](https://doi.org/10.5281/zenodo.7013396)

# Monte Carlo Integration

Theory and implementation of Monte Carlo integration in Python.

## Theory

See [docs/monte_carlo_integration.pdf](docs/monte_carlo_integration.pdf) for a write-up of my research notes.

## Example

Here is an example using indicator functions.

```python

import numpy as np

import mcintegration as mci

# Indicator function for being inside a unit sphere in R^N

i = lambda x: np.sum(x**2, -1) <= 1.0

# Area of unit circle in R^2

A_circle, err_one_sigma = mci.mcintegrate(

    i,

    lower=[-1.0] * 2,

    upper=[1.0] * 2,

    n=int(1e5),

)

print(A_circle, err_one_sigma)

# 3.1438 0.00129

# Volume of unit sphere in R^3

V_sphere, err_one_sigma = mci.mcintegrate(

    i,

    lower=[-1.0] * 3,

    upper=[1.0] * 3,

    n=int(1e5),

)

print(V_sphere, err_one_sigma)

# 4.1735 0.00157

```